Method and apparatus for design of a metrology target

ABSTRACT

A method of metrology target design is described. The method includes determining a sensitivity of a parameter for a metrology target design to an optical aberration, determining the parameter for a product design exposed using an optical system of a lithographic apparatus, and determining an impact on the parameter of the metrology target design based on the parameter for the product design and the product of the sensitivity and one or more of the respective aberrations of the optical system.

This application is a continuation of co-pending U.S. patent applicationSer. No. 14/577,820, filed Dec. 19, 2014, which claims the benefit ofpriority under 35 USC §119(e) of U.S. Provisional Patent Application No.61/921,874, filed Dec. 30, 2013, the entire disclosure of each of theforegoing applications is hereby incorporated by reference.

FIELD

The present description relates to methods and apparatus to determineone or more structural parameters of a metrology target usable, forexample, in the manufacture of devices by a lithographic technique andto methods of manufacturing using a lithographic technique.

BACKGROUND

A lithographic apparatus is a machine that applies a desired patternonto a substrate, usually onto a target portion of the substrate. Alithographic apparatus can be used, for example, in the manufacture ofintegrated circuits (ICs). In that instance, a patterning device, whichis alternatively referred to as a mask or a reticle, may be used togenerate a circuit pattern to be formed on an individual layer of theIC. This pattern can be transferred onto a target portion (e.g.,including part of, one, or several dies) on a substrate (e.g., a siliconwafer). Transfer of the pattern is typically via imaging onto a layer ofradiation-sensitive material (resist) provided on the substrate. Ingeneral, a single substrate will contain a network of adjacent targetportions that are successively patterned. Known lithographic apparatusinclude so-called steppers, in which each target portion is irradiatedby exposing an entire pattern onto the target portion at one time, andso-called scanners, in which each target portion is irradiated byscanning the pattern through a radiation beam in a given direction (the“scanning”-direction) while synchronously scanning the substrateparallel or anti parallel to this direction. It is also possible totransfer the pattern from the patterning device to the substrate byimprinting the pattern onto the substrate.

In lithographic processes, it is desirable to frequently makemeasurements of the structures created, e.g., for process control andverification. One or more parameters of the structures are typicallymeasured or determined, for example the overlay error between successivelayers formed in or on the substrate. There are various techniques formaking measurements of the microscopic structures formed in alithographic process. Various tools for making such measurements areknown, including scanning electron microscopes, which are often used tomeasure critical dimension (CD), and specialized tools to measureoverlay, the accuracy of alignment of two layers in a device. An exampleof such a tool is a scatterometer developed for use in the lithographicfield. This device directs a beam of radiation onto a target on thesurface of the substrate and measures one or more properties of theredirected radiation—e.g., intensity at a single angle of reflection asa function of wavelength; intensity at one or more wavelengths as afunction of reflected angle; or polarization as a function of reflectedangle—to obtain a “spectrum” from which a property of interest of thetarget can be determined. Determination of the property of interest maybe performed by various techniques: e.g., reconstruction of the targetstructure by iterative approaches such as rigorous coupled wave analysisor finite element methods, library searches, and principal componentanalysis.

SUMMARY

It is desirable, for example, to provide methods and apparatus fordesign of a metrology target. Furthermore, although not limited to this,it would be of advantage if the methods and apparatus could be appliedto minimizing overlay error in lithographic process.

In an aspect, there is provided a method of metrology target design. Themethod includes determining a sensitivity of a parameter for a metrologytarget design to each of a plurality of optical aberrations, determiningthe parameter for a product design exposed using an optical system of alithographic apparatus, and determining an impact on the parameter ofthe metrology target design based on the parameter for the productdesign and the product of the sensitivity and one or more of therespective aberrations of the optical system.

In an aspect, there is provided a method of metrology target design. Themethod includes determining a sensitivity of overlay error for ametrology target design to each of a plurality of aberrations, anddetermining an overlay error impact of the metrology target design basedon the sum of the sensitivities multiplied by the respective aberrationsof an optical system of a lithographic apparatus to expose the metrologytarget.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will now be described, by way of example only, withreference to the accompanying drawings in which:

FIG. 1 schematically depicts an embodiment of a lithographic apparatus;

FIG. 2 schematically depicts an embodiment of a lithographic cell orcluster;

FIG. 3 schematically depicts an embodiment of a scatterometer;

FIG. 4 schematically depicts a further embodiment of a scatterometer;

FIG. 5 schematically depicts a form of multiple grating target and anoutline of a measurement spot on a substrate;

FIGS. 6A and 6B schematically depict a model structure of one period ofan overlay target showing an example of variation of the target fromideal, e.g., two types of process-induced asymmetry;

FIG. 7 is an exemplary block diagram illustrating the functional modulesof a lithographic simulation model;

FIG. 8 schematically depicts a process for metrology target design; and

FIG. 9 schematically depicts a further process for metrology targetdesign.

DETAILED DESCRIPTION

Before describing embodiments in detail, it is instructive to present anexample environment in which embodiments may be implemented.

FIG. 1 schematically depicts a lithographic apparatus LA. The apparatuscomprises:

-   -   an illumination system (illuminator) IL configured to condition        a radiation beam B (e.g. DUV radiation or EUV radiation);    -   a support structure (e.g. a mask table) MT constructed to        support a patterning device (e.g. a mask) MA and connected to a        first positioner PM configured to accurately position the        patterning device in accordance with certain parameters;    -   a substrate table (e.g. a wafer table) WTa constructed to hold a        substrate (e.g. a resist-coated wafer) W and connected to a        second positioner PW configured to accurately position the        substrate in accordance with certain parameters; and    -   a projection system (e.g. a refractive projection lens system)        PS configured to project a pattern imparted to the radiation        beam B by patterning device MA onto a target portion C (e.g.        comprising one or more dies) of the substrate W.

The illumination system may include various types of optical components,such as refractive, reflective, magnetic, electromagnetic, electrostaticor other types of optical components, or any combination thereof, fordirecting, shaping, or controlling radiation.

The patterning device support structure holds the patterning device in amanner that depends on the orientation of the patterning device, thedesign of the lithographic apparatus, and other conditions, such as forexample whether or not the patterning device is held in a vacuumenvironment. The patterning device support structure can use mechanical,vacuum, electrostatic or other clamping techniques to hold thepatterning device. The patterning device support structure may be aframe or a table, for example, which may be fixed or movable asrequired. The patterning device support structure may ensure that thepatterning device is at a desired position, for example with respect tothe projection system. Any use of the terms “reticle” or “mask” hereinmay be considered synonymous with the more general term “patterningdevice.”

The term “patterning device” used herein should be broadly interpretedas referring to any device that can be used to impart a radiation beamwith a pattern in its cross-section such as to create a pattern in atarget portion of the substrate. It should be noted that the patternimparted to the radiation beam may not exactly correspond to the desiredpattern in the target portion of the substrate, for example if thepattern includes phase-shifting features or so called assist features.Generally, the pattern imparted to the radiation beam will correspond toa particular functional layer in a device being created in the targetportion, such as an integrated circuit.

The patterning device may be transmissive or reflective. Examples ofpatterning devices include masks, programmable mirror arrays, andprogrammable LCD panels. Masks are well known in lithography, andinclude mask types such as binary, alternating phase-shift, andattenuated phase-shift, as well as various hybrid mask types. An exampleof a programmable mirror array employs a matrix arrangement of smallmirrors, each of which can be individually tilted so as to reflect anincoming radiation beam in different directions. The tilted mirrorsimpart a pattern in a radiation beam, which is reflected by the mirrormatrix.

The term “projection system” used herein should be broadly interpretedas encompassing any type of projection system, including refractive,reflective, catadioptric, magnetic, electromagnetic and electrostaticoptical systems, or any combination thereof, as appropriate for theexposure radiation being used, or for other factors such as the use ofan immersion liquid or the use of a vacuum. Any use of the term“projection lens” herein may be considered as synonymous with the moregeneral term “projection system”.

As here depicted, the apparatus is of a transmissive type (e.g.,employing a transmissive mask). Alternatively, the apparatus may be of areflective type (e.g., employing a programmable mirror array of a typeas referred to above, or employing a reflective mask).

The lithographic apparatus may be of a type having two (dual stage) ormore tables (e.g., two or more substrate table, two or more patterningdevice support structures, or a substrate table and metrology table). Insuch “multiple stage” machines the additional tables may be used inparallel, or preparatory steps may be carried out on one or more tableswhile one or more other tables are being used for exposure.

The lithographic apparatus may also be of a type wherein at least aportion of the substrate may be covered by a liquid having a relativelyhigh refractive index, e.g., water, so as to fill a space between theprojection system and the substrate. An immersion liquid may also beapplied to other spaces in the lithographic apparatus, for example,between the mask and the projection system. Immersion techniques arewell known in the art for increasing the numerical aperture ofprojection systems. The term “immersion” as used herein does not meanthat a structure, such as a substrate, must be submerged in liquid, butrather only means that liquid is located between the projection systemand the substrate during exposure.

Referring to FIG. 1, the illuminator IL receives a radiation beam from aradiation source SO. The source and the lithographic apparatus may beseparate entities, for example when the source is an excimer laser. Insuch cases, the source is not considered to form part of thelithographic apparatus and the radiation beam is passed from the sourceSO to the illuminator IL with the aid of a beam delivery system BDincluding, for example, suitable directing mirrors and/or a beamexpander. In other cases the source may be an integral part of thelithographic apparatus, for example when the source is a mercury lamp.The source SO and the illuminator IL, together with the beam deliverysystem BD if required, may be referred to as a radiation system.

The illuminator IL may include an adjuster AD for adjusting the angularintensity distribution of the radiation beam. Generally, at least theouter and/or inner radial extent (commonly referred to as σ-outer andσ-inner, respectively) of the intensity distribution in a pupil plane ofthe illuminator can be adjusted. In addition, the illuminator IL mayinclude various other components, such as an integrator IN and acondenser CO. The illuminator may be used to condition the radiationbeam, to have a desired uniformity and intensity distribution in itscross section.

The radiation beam B is incident on the patterning device (e.g., mask)MA, which is held on the patterning device support (e.g., mask tableMT), and is patterned by the patterning device. Having traversed thepatterning device (e.g., mask) MA, the radiation beam B passes throughthe projection system PS, which focuses the beam onto a target portion Cof the substrate W. With the aid of the second positioner PW andposition sensor IF (e.g., an interferometric device, linear encoder, 2-Dencoder or capacitive sensor), the substrate table WTa can be movedaccurately, e.g., so as to position different target portions C in thepath of the radiation beam B. Similarly, the first positioner PM andanother position sensor (which is not explicitly depicted in FIG. 1) canbe used to accurately position the patterning device (e.g., mask) MAwith respect to the path of the radiation beam B, e.g., after mechanicalretrieval from a mask library, or during a scan. In general, movement ofthe patterning device support (e.g., mask table) MT may be realized withthe aid of a long-stroke module (coarse positioning) and a short-strokemodule (fine positioning), which form part of the first positioner PM.Similarly, movement of the substrate table WTa may be realized using along-stroke module and a short-stroke module, which form part of thesecond positioner PW. In the case of a stepper (as opposed to a scanner)the patterning device support (e.g., mask table) MT may be connected toa short-stroke actuator only, or may be fixed.

Patterning device (e.g., mask) MA and substrate W may be aligned usingmask alignment marks M1, M2 and substrate alignment marks P1, P2.Although the substrate alignment marks as illustrated occupy dedicatedtarget portions, they may be located in spaces between target portions(these are known as scribe-lane alignment marks). Similarly, insituations in which more than one die is provided on the patterningdevice (e.g., mask) MA, the mask alignment marks may be located betweenthe dies. Small alignment markers may also be included within dies, inamongst the device features, in which case it is desirable that themarkers be as small as possible and not require any different imaging orprocess conditions than adjacent features. The alignment system, whichdetects the alignment markers, is described further below.

The depicted apparatus could be used in at least one of the followingmodes:

1. In step mode, the patterning device support (e.g., mask table) MT andthe substrate table WTa are kept essentially stationary, while an entirepattern imparted to the radiation beam is projected onto a targetportion C at one time (i.e., a single static exposure). The substratetable WTa is then shifted in the X and/or Y direction so that adifferent target portion C can be exposed. In step mode, the maximumsize of the exposure field limits the size of the target portion Cimaged in a single static exposure.

2. In scan mode, the patterning device support (e.g., mask table) MT andthe substrate table WTa are scanned synchronously while a patternimparted to the radiation beam is projected onto a target portion C(i.e., a single dynamic exposure). The velocity and direction of thesubstrate table WTa relative to the patterning device support (e.g.,mask table) MT may be determined by the (de-)magnification and imagereversal characteristics of the projection system PS. In scan mode, themaximum size of the exposure field limits the width (in the non-scanningdirection) of the target portion in a single dynamic exposure, whereasthe length of the scanning motion determines the height (in the scanningdirection) of the target portion.

3. In another mode, the patterning device support (e.g., mask table) MTis kept essentially stationary holding a programmable patterning device,and the substrate table WTa is moved or scanned while a pattern impartedto the radiation beam is projected onto a target portion C. In thismode, generally a pulsed radiation source is employed and theprogrammable patterning device is updated as required after eachmovement of the substrate table WTa or in between successive radiationpulses during a scan. This mode of operation can be readily applied tomaskless lithography that utilizes programmable patterning device, suchas a programmable mirror array of a type as referred to above.

Combinations and/or variations on the above described modes of use orentirely different modes of use may also be employed.

Lithographic apparatus LA is of a so-called dual stage type which hastwo tables WTa, WTb (e.g., two substrate tables) and two stations—anexposure station and a measurement station—between which the tables canbe exchanged. For example, while a substrate on one table is beingexposed at the exposure station, another substrate can be loaded ontothe other substrate table at the measurement station and variouspreparatory steps carried out. The preparatory steps may include mappingthe surface control of the substrate using a level sensor LS andmeasuring the position of alignment markers on the substrate using analignment sensor AS, both sensors being supported by a reference frameRF. If the position sensor IF is not capable of measuring the positionof a table while it is at the measurement station as well as at theexposure station, a second position sensor may be provided to enable thepositions of the table to be tracked at both stations. As anotherexample, while a substrate on one table is being exposed at the exposurestation, another table without a substrate waits at the measurementstation (where optionally measurement activity may occur). This othertable has one or more measurement devices and may optionally have othertools (e.g., cleaning apparatus). When the substrate has completedexposure, the table without a substrate moves to the exposure station toperform, e.g., measurements and the table with the substrate moves to alocation (e.g., the measurement station) where the substrate is unloadedand another substrate is load. These multi-table arrangements enable asubstantial increase in the throughput of the apparatus.

As shown in FIG. 2, the lithographic apparatus LA forms part of alithographic cell LC, also sometimes referred to as a lithocell orlithocluster, which also includes apparatus to perform one or more pre-and post-exposure processes on a substrate. Conventionally these includeone or more spin coaters SC to deposit a resist layer, one or moredevelopers DE to develop exposed resist, one or more chill plates CH andone or more bake plates BK. A substrate handler, or robot, RO picks up asubstrate from input/output ports I/O1, I/O2, moves it between thedifferent process devices and delivers it to the loading bay LB of thelithographic apparatus. These devices, which are often collectivelyreferred to as the track, are under the control of a track control unitTCU which is itself controlled by the supervisory control system SCS,which also controls the lithographic apparatus via lithographic controlunit LACU. Thus, the different apparatus may be operated to maximizethroughput and processing efficiency.

In order that the substrate that is exposed by the lithographicapparatus is exposed correctly and consistently, it is desirable toinspect an exposed substrate to measure one or more properties such asoverlay error between subsequent layers, line thickness, criticaldimension (CD), etc. If an error is detected, an adjustment may be madeto an exposure of one or more subsequent substrates, especially if theinspection can be done soon and fast enough that another substrate ofthe same batch is still to be exposed. Also, an already exposedsubstrate may be stripped and reworked (to improve yield) or discarded,thereby avoiding performing an exposure on a substrate that is known tobe faulty. In a case where only some target portions of a substrate arefaulty, a further exposure may be performed only on those targetportions which are good. Another possibility is to adapt a setting of asubsequent process step to compensate for the error, e.g. the time of atrim etch step can be adjusted to compensate for substrate-to-substrateCD variation resulting from the lithographic process step.

An inspection apparatus is used to determine one or more properties of asubstrate, and in particular, how one or more properties of differentsubstrates or different layers of the same substrate vary from layer tolayer and/or across a substrate. The inspection apparatus may beintegrated into the lithographic apparatus LA or the lithocell LC or maybe a stand-alone device. To enable most rapid measurements, it isdesirable that the inspection apparatus measure one or more propertiesin the exposed resist layer immediately after the exposure. However, thelatent image in the resist has a very low contrast—there is only a verysmall difference in refractive index between the part of the resistwhich has been exposed to radiation and that which has not—and not allinspection apparatus have sufficient sensitivity to make usefulmeasurements of the latent image. Therefore measurements may be takenafter the post-exposure bake step (PEB) which is customarily the firststep carried out on an exposed substrate and increases the contrastbetween exposed and unexposed parts of the resist. At this stage, theimage in the resist may be referred to as semi-latent. It is alsopossible to make measurements of the developed resist image—at whichpoint either the exposed or unexposed parts of the resist have beenremoved—or after a pattern transfer step such as etching. The latterpossibility limits the possibility for rework of a faulty substrate butmay still provide useful information, e.g. for the purpose of processcontrol.

FIG. 3 depicts an embodiment of a scatterometer SM1. It comprises abroadband (white light) radiation projector 2 which projects radiationonto a substrate 6. The reflected radiation is passed to a spectrometerdetector 4, which measures a spectrum 10 (i.e. a measurement ofintensity as a function of wavelength) of the specular reflectedradiation. From this data, the structure or profile giving rise to thedetected spectrum may be reconstructed by processing unit PU, e.g. byRigorous Coupled Wave Analysis and non-linear regression or bycomparison with a library of simulated spectra as shown at the bottom ofFIG. 3. In general, for the reconstruction, the general form of thestructure is known and some parameters are assumed from knowledge of theprocess by which the structure was made, leaving only a few parametersof the structure to be determined from the scatterometry data. Such ascatterometer may be configured as a normal-incidence scatterometer oran oblique-incidence scatterometer.

Another embodiment of a scatterometer SM2 is shown in FIG. 4. In thisdevice, the radiation emitted by radiation source 2 is focused usinglens system 12 through interference filter 13 and polarizer 17,reflected by partially reflective surface 16 and is focused ontosubstrate W via a microscope objective lens 15, which has a highnumerical aperture (NA), desirably at least 0.9 or at least 0.95. Animmersion scatterometer may even have a lens with a numerical apertureover 1. The reflected radiation then transmits through partiallyreflective surface 16 into a detector 18 in order to have the scatterspectrum detected. The detector may be located in the back-projectedpupil plane 11, which is at the focal length of the lens 15, however thepupil plane may instead be re-imaged with auxiliary optics (not shown)onto the detector 18. The pupil plane is the plane in which the radialposition of radiation defines the angle of incidence and the angularposition defines the azimuth angle of the radiation. The detector isdesirably a two-dimensional detector so that a two-dimensional angularscatter spectrum (i.e. a measurement of intensity as a function of angleof scatter) of the substrate target can be measured. The detector 18 maybe, for example, an array of CCD or CMOS sensors, and may have anintegration time of, for example, 40 milliseconds per frame.

A reference beam is often used, for example, to measure the intensity ofthe incident radiation. To do this, when the radiation beam is incidenton the partially reflective surface 16 part of it is transmitted throughthe surface as a reference beam towards a reference mirror 14. Thereference beam is then projected onto a different part of the samedetector 18.

One or more interference filters 13 are available to select a wavelengthof interest in the range of, say, 405-790 nm or even lower, such as200-300 nm. The interference filter(s) may be tunable rather thancomprising a set of different filters. A grating could be used insteadof or in addition to one or more interference filters.

The detector 18 may measure the intensity of scattered radiation at asingle wavelength (or narrow wavelength range), the intensity separatelyat multiple wavelengths or the intensity integrated over a wavelengthrange. Further, the detector may separately measure the intensity oftransverse magnetic—(TM) and transverse electric—(TE) polarizedradiation and/or the phase difference between the transverse magnetic-and transverse electric-polarized radiation.

Using a broadband radiation source 2 (i.e. one with a wide range ofradiation frequencies or wavelengths—and therefore of colors) ispossible, which gives a large etendue, allowing the mixing of multiplewavelengths. The plurality of wavelengths in the broadband desirablyeach has a bandwidth of δλ and a spacing of at least 2δλ (i.e. twice thewavelength bandwidth). Several “sources” of radiation may be differentportions of an extended radiation source which have been split using,e.g., fiber bundles. In this way, angle resolved scatter spectra may bemeasured at multiple wavelengths in parallel. A 3-D spectrum (wavelengthand two different angles) may be measured, which contains moreinformation than a 2-D spectrum. This allows more information to bemeasured which increases metrology process robustness. This is describedin more detail in U.S. patent application publication no. US2006-0066855, which document is hereby incorporated in its entirety byreference.

By comparing one or more properties of the beam before and after it hasbeen redirected by the target, one or more properties of the substratemay be determined. This may be done, for example, by comparing theredirected beam with theoretical redirected beams calculated using amodel of the substrate and searching for the model that gives the bestfit between measured and calculated redirected beams. Typically aparameterized generic model is used and the parameters of the model, forexample width, height and sidewall angle of the pattern, are varieduntil the best match is obtained.

Two main types of scatterometer are used. A spectroscopic scatterometerdirects a broadband radiation beam onto the substrate and measures thespectrum (intensity as a function of wavelength) of the radiationscattered into a particular narrow angular range. An angularly resolvedscatterometer uses a monochromatic radiation beam and measures theintensity (or intensity ratio and phase difference in case of anellipsometric configuration) of the scattered radiation as a function ofangle. Alternatively, measurement signals of different wavelengths maybe measured separately and combined at an analysis stage. Polarizedradiation may be used to generate more than one spectrum from the samesubstrate.

In order to determine one or more parameters of the substrate, a bestmatch is typically found between the theoretical spectrum produced froma model of the substrate and the measured spectrum produced by theredirected beam as a function of either wavelength (spectroscopicscatterometer) or angle (angularly resolved scatterometer). To find thebest match there are various methods, which may be combined. Forexample, a first method is an iterative search method, where a first setof model parameters is used to calculate a first spectrum, a comparisonbeing made with the measured spectrum. Then a second set of modelparameters is selected, a second spectrum is calculated and a comparisonof the second spectrum is made with the measured spectrum. These stepsare repeated with the goal of finding the set of parameters that givesthe best matching spectrum. Typically, the information from thecomparison is used to steer the selection of the subsequent set ofparameters. This process is known as an iterative search technique. Themodel with the set of parameters that gives the best match is consideredto be the best description of the measured substrate.

A second method is to make a library of spectra, each spectrumcorresponding to a specific set of model parameters. Typically the setsof model parameters are chosen to cover all or almost all possiblevariations of substrate properties. The measured spectrum is compared tothe spectra in the library. Similarly to the iterative search method,the model with the set of parameters corresponding to the spectrum thatgives the best match is considered to be the best description of themeasured substrate. Interpolation techniques may be used to determinemore accurately the best set of parameters in this library searchtechnique.

In any method, sufficient data points (wavelengths and/or angles) in thecalculated spectrum should be used in order to enable an accurate match,typically between 80 up to 800 data points or more for each spectrum.Using an iterative method, each iteration for each parameter value wouldinvolve calculations at 80 or more data points. This is multiplied bythe number of iterations needed to obtain the correct profileparameters. Thus many calculations may be required. In practice thisleads to a compromise between accuracy and speed of processing. In thelibrary approach, there is a similar compromise between accuracy and thetime required to set up the library.

In any of the scatterometers described above, the target on substrate Wmay be a grating which is printed such that after development, the barsare formed of solid resist lines. The bars may alternatively be etchedinto the substrate. The target pattern is chosen to be sensitive to aparameter of interest, such as focus, dose, overlay, chromaticaberration in the lithographic projection apparatus, etc., such thatvariation in the relevant parameter will manifest as variation in theprinted target. For example, the target pattern may be sensitive tochromatic aberration in the lithographic projection apparatus,particularly the projection system PL, and illumination symmetry and thepresence of such aberration will manifest itself in a variation in theprinted target pattern. Accordingly, the scatterometry data of theprinted target pattern is used to reconstruct the target pattern. Theparameters of the target pattern, such as line width and shape, may beinput to the reconstruction process, performed by a processing unit PU,from knowledge of the printing step and/or other scatterometryprocesses.

While embodiments of a scatterometer have been described herein, othertypes of metrology apparatus may be used in an embodiment. For example,a dark field metrology apparatus such as described in U.S. PatentApplication Publication No. 2013-0308142, which is incorporated hereinin its entirety by reference, may be used. Further, those other types ofmetrology apparatus may use a completely different technique thanscatterometry.

FIG. 5 depicts an example composite metrology target formed on asubstrate according to known practice. The composite target comprisesfour gratings 32, 33, 34, 35 positioned closely together so that theywill all be within a measurement spot 31 formed by the illumination beamof the metrology apparatus. The four targets thus are all simultaneouslyilluminated and simultaneously imaged on sensor 4, 18. In an examplededicated to overlay measurement, gratings 32, 33, 34, 35 are themselvescomposite gratings formed by overlying gratings that are patterned indifferent layers of the semi-conductor device formed on substrate W.Gratings 32, 33, 34, 35 may have differently biased overlay offsets inorder to facilitate measurement of overlay between the layers in whichthe different parts of the composite gratings are formed. Gratings 32,33, 34, 35 may also differ in their orientation, as shown, so as todiffract incoming radiation in X and Y directions. In one example,gratings 32 and 34 are X-direction gratings with biases of +d, −d,respectively. This means that grating 32 has its overlying componentsarranged so that if they were both printed exactly at their nominallocations, one of the components would be offset relative to the otherby a distance d. Grating 34 has its components arranged so that ifperfectly printed there would be an offset of d, but in the oppositedirection to the first grating and so on. Gratings 33 and 35 may beY-direction gratings with offsets +d and −d respectively. While fourgratings are illustrated, another embodiment may include a larger matrixto obtain desired accuracy. For example, a 3×3 array of nine compositegratings may have biases −4d, −3d, −2d, −d, 0, +d, +2d, +3d, +4d.Separate images of these gratings can be identified in the imagecaptured by sensor 4, 18.

The metrology targets as described herein may be, for example, overlaytargets designed for use with a metrology tool such as Yieldstarstand-alone or integrated metrology tool, and/or alignment targets suchas those typically used with a TwinScan lithographic system, bothavailable from ASML.

In general, metrology targets for use with such systems should beprinted on the substrate with dimensions that meet the designspecification for the particular microelectronic device to be imaged onthat substrate. As processes continue to push against the limits oflithographic device imaging resolution in advanced process nodes, thedesign rule and process compatibility requirements place stress on theselection of appropriate targets. As the targets themselves become moreadvanced, often requiring the use of resolution enhancement technology,such as phase-shift patterning devices, and optical proximitycorrection, the printability of the target within the process designrules becomes less certain. As a result, proposed metrology targetdesign may be subject to testing and/or simulation in order to confirmtheir suitability and/or viability, both from a printability and adetectability standpoint. In a commercial environment, good overlay markdetectability may be considered to be a combination of low totalmeasurement uncertainty as well as a short move-acquire-move time, asslow acquisition is detrimental to total throughput for the productionline. Modern micro-diffraction-based-overlay targets (μDBO) may be onthe order of 10 μm on a side, which provides an inherently low detectionsignal compared to 40×160 μm² targets such as those used in the contextof monitor substrates.

Additionally, once metrology targets that meet the above criteria havebeen selected, there is a possibility that detectability will changewith respect to process variations, such as film thickness variation,various etch biases, and geometry asymmetries induced by the etch and/orpolish processes. Therefore, it may be useful to select a target thathas low detectability variation and low overlay/alignment variationagainst various process variations. Likewise, the fingerprint (printingcharacteristics, including, for example, lens aberration) of thespecific machine that is to be used to produce the microelectronicdevice to be imaged will, in general, affect the imaging and productionof the metrology targets. It may therefore be useful to ensure that themetrology targets are resistant to fingerprint effects, as some patternswill be more or less affected by a particular lithographic fingerprint.

FIGS. 6A and 6B schematically show a model structure of one period of anoverlay target showing an example of variation of the target from ideal,e.g., two types of process-induced asymmetry. With reference to FIG. 6A,the substrate W is patterned with a bottom grating 700, etched into asubstrate layer. The etch process used for the bottom grating results ina tilt of the floor 702 of the etched trench. This floor tilt, FT, canbe represented as a structural parameter, for example as a measure ofthe height drop across the floor 702, in nm. A BARC (bottomanti-reflective coating) layer 704 supports the patterned resist featureof the top grating 706. In this example, the alignment overlay errorbetween the top and bottom grating is zero, as the centers of the topand bottom grating features are at the same lateral position. However,the bottom-layer process-induced asymmetry, i.e. the floor tilt, leadsto an error in the measured overlay offset, in this case giving anon-zero overlay offset. FIG. 6B shows another type of bottom-layerprocess-induced asymmetry that can lead to an error in the measuredoverlay offset. This is side wall angle (SWA) unbalance, SWAun. Featuresin common with those of FIG. 6A are labeled the same. Here, one sidewall 708 of the bottom grating has a different slope to the other sidewall 710. This unbalance can be represented as a structural parameter,for example as a ratio of the two side wall angles relative to the planeof the substrate. Both asymmetry parameters floor tilt and SWA unbalancegive rise to an “apparent” overlay error between the top and bottomgratings. This apparent overlay error comes on top of the “real” overlayerror to be measured between the top and bottom gratings.

Accordingly, in an embodiment, it is desirable to simulate variousmetrology target designs in order to confirm the suitability and/orviability of one or more of the proposed target designs.

In a system for simulating a manufacturing process involving lithographyand metrology targets, the major manufacturing system components and/orprocesses can be described by various functional modules, for example,as illustrated in FIG. 7. Referring to FIG. 7, the functional modulesmay include a design layout module 71, which defines a metrology target(and/or microelectronic device) design pattern; a patterning devicelayout module 72, which defines how the patterning device pattern islaid out in polygons based on the target design; a patterning devicemodel module 73, which models the physical properties of the pixilatedand continuous-tone patterning device to be utilized during thesimulation process; an optical model module 74, which defines theperformance of the optical components of the lithography system; aresist model module 75, which defines the performance of the resistbeing utilized in the given process; a process model module 76, whichdefines performance of the post-resist development processes (e.g.,etch); and metrology module 77, which defines the performance of ametrology system used with the metrology target and thus the performanceof the metrology target when used with the metrology system. The resultsof one or more of the simulation modules, for example, predictedcontours and CDs, are provided in a result module 78.

The properties of the illumination and projection optics are captured inthe optical model module 74 that includes, but is not limited to,NA-sigma (□) settings as well as any particular illumination sourceshape, where □ (or sigma) is outer radial extent of the illuminator. Theoptical properties of the photo-resist layer coated on a substrate—i.e.refractive index, film thickness, propagation and polarizationeffects—may also be captured as part of the optical model module 74,whereas the resist model module 75 describes the effects of chemicalprocesses which occur during resist exposure, post exposure bake (PEB)and development, in order to predict, for example, contours of resistfeatures formed on the substrate. The patterning device model module 73captures how the target design features are laid out in the pattern ofthe patterning device and may include a representation of detailedphysical properties of the patterning device, as described, for example,in U.S. Pat. No. 7,587,704. The objective of the simulation is toaccurately predict, for example, edge placements and critical dimensions(CDs), which can then be compared against the target design. The targetdesign is generally defined as the pre-OPC patterning device layout, andwill be provided in a standardized digital file format such as GDSII orOASIS.

In general, the connection between the optical and the resist model is asimulated aerial image intensity within the resist layer, which arisesfrom the projection of radiation onto the substrate, refraction at theresist interface and multiple reflections in the resist film stack. Theradiation intensity distribution (aerial image intensity) is turned intoa latent “resist image” by absorption of photons, which is furthermodified by diffusion processes and various loading effects. Efficientsimulation methods that are fast enough for full-chip applicationsapproximate the realistic 3-dimensional intensity distribution in theresist stack by a 2-dimensional aerial (and resist) image.

Thus, the model formulation describes most, if not all, of the knownphysics and chemistry of the overall process, and each of the modelparameters desirably corresponds to a distinct physical or chemicaleffect. The model formulation thus sets an upper bound on how well themodel can be used to simulate the overall manufacturing process.However, sometimes the model parameters may be inaccurate frommeasurement and reading errors, and there may be other imperfections inthe system. With precise calibration of the model parameters, extremelyaccurate simulations can be done.

In a manufacturing process, variations in various process parametershave significant impact on the design of a suitable target that canfaithfully reflect a product design. Such process parameters include,but are not limited to, side-wall angle (determined by the etching ordevelopment process), refractive index (of a device layer or a resistlayer), thickness (of a device layer or a resist layer), frequency ofincident radiation, etch depth, floor tilt, extinction coefficient forthe radiation source, coating asymmetry (for a resist layer or a devicelayer), variation in erosion during a chemical-mechanical polishingprocess, and the like.

A metrology target design can be characterized by various parameterssuch as, for example, target coefficient (TC), stack sensitivity (SS),overlay impact (OV), or the like. Stack sensitivity measures the changein intensity with change in overlay because of diffraction betweentarget (e.g., grating) layers. Target coefficient measures the noisefrom the measurement system and can be thought of as equivalent of asignal to noise ratio for the metrology target. Target coefficient canalso be thought of as the ratio of stack sensitivity to photon noise.Overlay impact measures the change in overlay error as a function oftarget design.

As noted above, there may be various model parameters that can affect ordefine the selection of a particular metrology target design. Forexample, one or more geometric dimensions can be defined for aparticular target design such as pitch, critical dimension of a featureof the metrology target design, etc.

One of the model parameters may be an optical aberration of a systemused to transfer the metrology target design to a substrate; theprojection system PL used to image the metrology target (and/or, forexample, an electronic device pattern) may have an optical transferfunction that is non-uniform, which can affect the pattern imaged on thesubstrate W. There are various ways that such a parameter can beexpressed. For an optical model, a convenient way to define aberrationis through a set of Zernike polynomials. Zernike polynomials form a setof orthogonal polynomials defined on a unit circle. In the presentdisclosure, Zernikes are used as a non-limiting example for amethodology for designing metrology targets. However, it is to be notedthat the design methodology described herein can be extended to anyother aberration basis with similar characteristics.

In an embodiment, for unpolarized radiation, aberration effects can befairly well described by two scalar maps, which describe thetransmission (apodization) and relative phase (aberration) of radiationexiting the projection system PL as a function of position in a pupilplane thereof. These scalar maps, which may be referred to as thetransmission map and the relative phase map, may be expressed as alinear combination of a complete set of basis functions. A determinationof each scalar map may involve determining the coefficients in such anexpansion. Since the Zernike polynomials are orthogonal on the unitcircle, the Zernike coefficients may be determined by calculating theinner product of a measured scalar map with each Zernike polynomial inturn and dividing this by the square of the norm of that Zernikepolynomial.

The methodology disclosed herein provides an approach for designingmetrology targets based on sensitivity of a design parameter to one ormore Zernikes. As a background, aberration expressed as Zernike terms,Hopkins theory and transmission cross coefficients (TCC) is brieflydiscussed here. An aerial image AI can be expressed as:

AI(x, y) = ∑_(k₁, k₂)A(k₁, k₂)∑_(k₁^(′), k₂^(′))M(k₁^(′) − k₁, k₂^(′) − k₂)L(k₁^(′), k₂^(′))exp (−jk₁^(′)x − jk₂^(′)y)² = ∑_(k₁, k₂)[A(k₁, k₂)²[∑_(k₁^(′), k₂^(′))∑_(k₁^(″), k₂^(″))M(k₁^(′) − k₁, k₂^(′) − k₂)L(k₁^(′), k₂^(′))M^(*)(k₁^(″) − k₁, k₂^(″) − k₂)L^(*)(k₁^(″), k₂^(″))exp (−j(k₁^(′) − k₁^(″))x − j(k₂^(′) − k₂^(″))y)]] = ∑_(k₁^(′), k₂^(′), k₁^(″), k₂^(″))[[∑_(k₁, k₂)A(k₁, k₂)²L(k₁ + k₁^(′), k₂ + k₂^(′))L^(*)(k₁ + k₁^(″), k₂ + k₂^(″))]M(k₁^(′), k₂^(′))M^(*)(k₁^(″), k₂^(″))exp (−j(k₁^(′) − k₁^(″))x − j(k₂^(′) − k₂^(″))y)] = ∑_(k₁^(′), k₂^(′), k₁^(″), k₂^(″))[TCC_(k₁^(′), k₂^(′), k₁^(″), k₂^(″))M(k₁^(′), k₂^(′))M^(*)(k₁^(″), k₂^(″))exp (−    j(k₁^(′) − k₁^(″))x − j(k₂^(′) − k₂^(″))y)]whereinTCC_(k₁^(′), k₂^(′), k₁^(″), k₂^(″)) ≡ ∑_(k₁, k₂)A(k₁, k₂)²L(k₁ + k₁^(′), k₂ + k₂^(′))L^(*)(k₁ + k₁^(″), k₂ + k₂^(″))

where AI(x,y) is the aerial image in the space domain, A(k₁,k₂) is thesource amplitude from point k on the source pupil plane and L(k₁,k₂) isthe projection optics amplitude and phase function for point (k₁,k₂) onthe optical system pupil plane, also referred as “pupil image” in thisdisclosure. The projection optics function in the space domainrepresents distortions caused by the projection optics to the radiationpassing through the projection optics (e.g., distortions in amplitude,phase or both) as a function of location. M(k₁,k₂) is the patterningdevice function (i.e., design layout function) in the spatial frequencydomain, and can be obtained from the patterning device function in thespace domain by a Fourier transform. The patterning device function inthe space domain represents distortions caused by the patterning deviceto the radiation passing via the patterning device (e.g., distortions inamplitude, phase or both) as a function of location. More details can befound in, for example, in U.S. Pat. No. 7,587,704, which is incorporatedby reference in its entirety. A function in the space domain can betransformed to a corresponding function in the spatial frequency domainand vice versa by Fourier transform. Here, x and k are both vectors. Itis further noted that although in the given example, the equations aboveare derived from a scalar imaging model, this formalism can also beextended to a vector imaging model, where TE and TM or other polarizedradiation components are summed separately.

TCC_(k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″) can be viewed as a matrix,which includes optical properties of the lithographic projectionapparatus excluding the patterning device. Also note that the TCC matrixis Hermitian, i.e., TCC_(k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″)=TCC*_(k) ₁_(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″).

Computation of the aerial image using the above equations can besimplified if only dominant eigenvalues of TCC_(k) ₁ _(′,k) ₂ _(′,k) ₁_(″,k) ₂ _(″) are used. Specifically, when TCC_(k) ₁ _(′,k) ₂ _(′,k) ₁_(″,k) ₂ _(″) is diagonalized and the largest R eigenvalues areretained, the TCC_(k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″) can beapproximated as:

${TCC}_{k_{1}^{\prime},k_{2}^{\prime},k_{1}^{''},k_{2}^{''}} = {\sum\limits_{r = 1}^{R}\; {\lambda_{r}{\varphi_{r}\left( {k_{1}^{\prime},k_{2}^{\prime}} \right)}{\varphi_{r}^{*}\left( {k_{1}^{''},k_{2}^{''}} \right)}}}$

wherein λ_(r) (r=1, K, R) are the R largest eigenvalues and φ_(r) is theeigenvector corresponding to the eigenvalue λ_(r).

In a practical lithographic projection apparatus, for Zernikecoefficient z_(n), TCC_(k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″) can be wellapproximated as TCC_(k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″)(z_(n))≈TCC_(k)₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″)(z_(n0))+a_(TCC,n,k) ₁ _(′,k) ₂ _(′,k)₁ _(″,k) ₂ _(″)(z_(n)−z_(n0))+b_(TCC,n,k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂_(″)(z_(n)−z_(n0))² TCC_(k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″)(z_(n0)),a_(TCC,n,k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″) and b_(TCC,n,k) ₁ _(′,k) ₂_(′,k) ₁ _(″,k) ₂ _(″) are independent from z_(n). Therefore, onceTCC_(k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″)(z_(n0)), a_(TCC,n,k) ₁ _(′,k)₂ _(′,k) ₁ _(″,k) ₂ _(″) and b_(TCC,n,k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂_(″) are computed, TCC_(k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″)(z_(n)) as afunction of z_(n) is known. TCC_(k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂_(″)(z_(n0)) can be directly calculated from the nominal conditionz_(n)=z_(n0). The coefficients a_(TCC,n,k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂_(″), and b_(TCC,n,k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″) can be fittedfrom a set of known values of z_(n) or be derived as partialderivatives, details of which can be found in commonly assigned U.S.Patent Application Publication No. 2009-0157360, the disclosure of whichis hereby incorporated by reference in its entirety.

Once TCC_(k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″)(z_(n0)), a_(TCC,n,k) ₁_(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″) and b_(TCC,n,k) ₁ _(′,k) ₂ _(′,k) ₁_(″,k) ₂ _(″) are computed, the computation of the aerial image AI canbe further simplified using an expansion with respect to z_(n):

AI(zn)≈AI(z _(n0))+a _(I,n)(z _(n) −z _(n0))+b _(I,n)(z _(n) −z _(n0))²

Note that AI(z_(n0)), a_(I,n), and b_(I,n) are referred to aspseudo-aerial images, which can be computed from the patterning deviceimage and TCC_(k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″)(z_(n0)), a_(TCC,n,k)₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″), and b_(TCC,n,k) ₁ _(′,k) ₂ _(′,k) ₁_(″,k) ₂ _(″) respectively. Further, note that these pseudo-aerialimages are all independent of z_(n).

For optics with pupil image L(k₁, k₂) and A(k₁, k₂), the resulting TCCis:

TCC_(k) ₁ _(′,k) ₂ _(′,k) ₁ _(″,k) ₂ _(″)=Σ_(k) ₁ _(,k) ₂ [A(k ₁ ,k ₂)²L(k ₁ +k ₁ ′,k ₂ +k ₂′)L*(k ₁ +k ₁ ″,k ₂ +k ₂″)]

With Zernike coefficient z_(n), the pupil image is expressed as:

L(k ₁ ,k ₂)=L ₀(k ₁ ,k ₂)exp(j(z _(n) −z _(n0))P _(n)(k ₁ ,k ₂)),

where L₀(k₁,k₂) is the nominal pupil image for z_(n)=z_(n0), andP_(n)(k₁, k₂) is the kernel image (or Zernike polynomial) correspondingto z_(n). To simplify the notation, we assume without loss of generalitythat z_(n0)=0, i.e., L(k₁,k₂)=L₀(k₁,k₂)exp(jz_(n)P_(n)(k₁,k₂)). Theskilled artisan will appreciate that all the discussions are valid fornon-zero z_(n0). It is also assumed that the nominal condition is set sothat all z_(n0)=0, therefore L₀(k₁,k₂) is aberration free except that itmay have defocus. As a result, L₀(k₁,k₂) is rotational symmetry, i.e.,for any two frequency pairs, (k₁′, k₂′) and (k₁″,k₂″),L₀(k₁′,k₂′)=L₀(k₁″,k₂″) whenever k₁′²+k₂′²=k₁″²+k₂″².

The TCC fitting process can be viewed as a Taylor expansion, where,

${{TCC}_{k_{1}^{\prime},k_{2}^{\prime},k_{1}^{''},k_{2}^{''}}\left( z_{n} \right)} = {{{TCC}_{k_{1}^{\prime},k_{2}^{\prime},k_{1}^{''},{k_{2}^{''}''}}\left( {z_{n} = 0} \right)} + {\frac{\partial{TCC}_{k_{1}^{\prime},k_{2}^{\prime},k_{1}^{''},k_{2}^{''}}}{\partial z_{n}}{_{z_{n} = 0}\mspace{14mu} {z_{n} + {\frac{1}{2}\frac{\partial^{2}{TCC}_{k_{}^{\prime},k_{2}^{\prime},k_{}^{''},k_{2}^{''}}}{\partial z_{n}^{2}}}}}_{z_{n} = 0}\mspace{14mu} z_{n}^{2}}}$

This implies that:

$\mspace{20mu} {a_{{TCC},n,k_{1}^{\prime},k_{2}^{\prime},k_{1}^{''},k_{2}^{''}} = {{\frac{\partial{TCC}_{k_{1}^{\prime},k_{2}^{\prime},k_{1}^{''},k_{2}^{''}}}{\partial z_{n}}_{z_{n} = 0}} = {{{\frac{\partial}{\partial z_{n}}\left( {\sum_{k_{1},k_{2}}\left\lbrack {{A\left( {k_{1},k_{2}} \right)}^{2}{L\left( {{k_{1} + k_{1}^{\prime}},{k_{2} + k_{2}^{\prime}}} \right)}{L^{*}\left( {{k_{1} + k_{1}^{''}},{k_{2} + k_{2}^{''}}} \right)}} \right\rbrack} \right)}_{z_{n} = 0}} = {\frac{\partial}{\partial z_{n}}\left( {\sum_{k_{1},k_{2}}\left\lbrack {{{{A\left( {k_{1},k_{2}} \right)}^{2} {L_{0}\left( {{k_{1} + k_{1}^{\prime}}, {k_{2} + k_{2}^{\prime}}} \right)} {L_{0}^{*}\left( {k_{1} + {\left. \quad{k_{1}^{''},{k_{2} + k_{2}^{''}}} \right) {\exp\left( {{jz}_{n}\left( {{P_{n}\left( {{k_{1} + k_{1}^{\prime}}, {k_{2} + k_{2}^{\prime}}} \right)} - \left. \quad{P_{n}\left( {{k_{1} + k_{1}^{''}},{k_{2} + k_{2}^{''}}} \right)} \right)} \right)} \right\rbrack}}} \right)}}_{z_{n} = 0}} = {{{\frac{\partial}{\partial z_{n}}\left( {\sum_{k_{1},k_{2}}\left\lbrack {{A\left( {k_{1},k_{2}} \right)}^{2} {L_{0}\left( {{k_{1} + k_{1}^{\prime}}, {k_{2} + k_{2}^{\prime}}} \right)} {L_{0}^{*}\left( {{k_{1} + k_{1}^{''}}, {k_{2} + k_{2}^{''}}} \right)} {\exp\left( {{jz}_{n}\left( {{P_{n}\left( {{k_{1} + k_{1}^{\prime}},{k_{2} + k_{2}^{\prime}}} \right)} - {P_{n}\left( {{k_{1} + k_{1}^{''}},{k_{2} + k_{2}^{''}}} \right)}} \right)} \right)}} \right\rbrack} \right)}_{z_{n} = 0}} = {{\sum_{k_{1},k_{2}}{\left\lbrack {{j\left( {{P_{n}\left( {{k_{1} + k_{1}^{\prime}},{k_{2} + k_{2}^{\prime}}} \right)} - {P_{n}\left( {{k_{1} + k_{1}^{''}},{k_{2} + k_{2}^{''}}} \right)}} \right)} {A\left( {k_{1},k_{2}} \right)}^{2} {L_{0}\left( {{k_{1} + k_{1}^{\prime}},{k_{2} + k_{2}^{\prime}}} \right)}{L_{0}^{*}\left( {{k_{1} + k_{1}^{''}},{k_{2} + k_{2}^{''}}} \right)}} \right\rbrack \mspace{20mu} b_{{TCC},n,k_{1}^{\prime},k_{2}^{\prime},k_{1}^{''},k_{2}^{''}}}} = {{{\frac{1}{2}\frac{\partial^{2}{TCC}_{k_{1}^{\prime},k_{2}^{\prime},k_{1}^{''},k_{2}^{''}}}{\partial z_{n}^{2}}}_{z_{n} = 0}} = {{{\frac{1}{2}\frac{\partial^{2}}{\partial z_{n}^{2}} \left( {\sum_{k_{1},k_{2}}\left\lbrack {{A\left( {k_{1},k_{2}} \right)}^{2} {L\left( {{k_{1} + k_{1}^{\prime}}, {k_{2} + k_{2}^{\prime}}} \right)} {L^{*}\left( {{k_{1} + k_{1}^{''}}, {k_{2} + k_{2}^{''}}} \right)}} \right\rbrack} \right)}_{z_{n} = 0}} = {\frac{1}{2}\frac{\partial^{2}}{\partial z_{n}^{2}}\left( {\sum_{k_{1},k_{2}}\left\lbrack {{A\left( {k_{1},k_{2}} \right)}^{2}{L_{0}\left( {{{k_{1} + \left. \quad{k_{1}^{\prime},{k_{2} + {\left. \quad k_{2}^{\prime} \right){L_{0}^{*}\left( {k_{1} + {\left. \quad{k_{1}^{*},{k_{2} + k_{2}^{''}}} \right) {\exp\left( {{jz}_{n}\left( {{P_{n}\left( {{k_{1} + k_{1}^{\prime}},{k_{2} + k_{2}^{\prime}}} \right)} - {P_{n}\left( {{k_{1} + k_{1}^{''}},{k_{2} + k_{2}^{''}}} \right)}} \right)} \right)}}} \right\rbrack}}}} \right)}_{z_{n = 0}}} = {{- \frac{1}{2}}{\sum_{k_{1},k_{2}}\left\lbrack \left( {{P_{n}\left( {{k_{1} + k_{1}^{\prime}},{k_{2} + k_{2}^{\prime}}} \right)} - {{P_{n}\left( {k_{1} + \left. \quad{k_{1}^{''},{k_{2} + k_{2}^{''}}} \right)} \right)}^{2} {A\left( {k_{1},k_{2}} \right)}^{2} {L_{0}\left( {k_{1} + {\left. \quad{k_{1}^{\prime},{k_{2} + k_{2}^{\prime}}} \right){L_{0}^{*}\left( {{k_{1} + k_{1}^{*}},{k_{2} + k_{2}^{*}}} \right)}}} \right\rbrack}}} \right. \right.}}} \right.}} \right.} \right.}}}}}} \right.} \right.}}}}$

In U.S Patent Application Publication No. 2013-0014065, which isincorporated herein by reference in its entirety, a method of designinga set of test patterns for being imaged via a projection lithographysystem is described, the set of test patterns comprising a lithographyresponse parameter related to a predefined wavefront aberration term ofthe projection lithography system, the predefined wavefront aberrationterm mathematically representing a characteristic of a wavefrontaberration, the method comprising: a) generating a mathematical seriesexpansion as an approximation of the lithography response parameter as afunction of the predefined wavefront aberration term; b) selecting a setof selected expansion terms from the mathematical series expansion; c)generating a cost function comprising the selected expansion terms; andd) solving the cost function to define the parameter of the set of testpatterns while constraining at least part of the unselected expansionterms substantially to zero. A set of test patterns for being imaged viaa projection lithography system may be designed according to theforegoing method for generating a predefined response on a variation ofthe predefined wavefront aberration term, wherein the predefinedresponse is substantially linear.

A metrology target design can be characterized by various parameterssuch as, for example, target coefficient (TC), stack sensitivity (SS),overlay impact (OV), or the like. Stack sensitivity can be understood asa measurement of how much the intensity of the signal changes as overlaychanges because of diffraction between target (e.g., grating) layers.Target coefficient can be understood as a measurement of signal-to-noiseratio for a particular measurement time as a result of variations inphoton collection by the measurement system. In an embodiment, thetarget coefficient can also be thought of as the ratio of stacksensitivity to photon noise; that is, the signal (i.e., the stacksensitivity) may be divided by a measurement of the photon noise todetermine the target coefficient. Overlay impact measures the change inoverlay error as a function of target design.

In a given optical system, more particularly for a given lithographicapparatus, the optical aberration resulting from various opticalelements of the lithographic apparatus may vary for different positions,i, across the imaging slit of the lithographic apparatus when exposingthe metrology target using the lithographic apparatus and when exposinga product (e.g., device) pattern using the lithographic apparatus. Ithas been discovered that within the normal range of lithographicapparatus aberration variations, variation in a particular parameter,par, characterizing a metrology target can be considered to be linearlydependent on the Zernike z_(n) at a particular position, i, across theimaging slit of the lithographic apparatus as, for example:

$\begin{matrix}{{\partial{par}} = {\sum_{n}{{z_{n}()} \cdot \frac{\partial{par}}{\partial z_{n}}}}} & (1)\end{matrix}$

where

$\frac{\partial{par}}{\partial z_{n}}$

can be considered as the sensitivity of the parameter to the particularZernike z_(n). It has been further discovered that the sensitivity ofthe parameter to a particular Zernike z_(n) is substantially independentof the slit position and of the lithographic apparatus. Accordingly, itis possible to determine the sensitivity

$\frac{\partial{par}}{\partial z_{n}}$

for the one or more Zernikes z_(n) and use those sensitivities fordifferent slit positions and/or different lithographic apparatuses(e.g., different aberration values and/or different aberrationprofiles).

In various embodiments, the sensitivity of the one or more parametersmay be measured or simulated. For example, in an embodiment, aberrationperturbation (“meander”) experiments may be performed to determine thesensitivity. As an example, during substrate exposure, the projectionsystem in the lithographic apparatus may be slightly heated, causingdeformation of one or more optical elements of the projection system andthus optical aberration. A lithographic apparatus may have controlmechanisms to reduce such aberration. But, when the control is switchedoff, the aberration is expected to be large enough to cause, forexample, measurable overlay error in product patterns as well as inmetrology targets. The amount of aberration can be measured ordetermined by a sensor in the lithographic apparatus and the parameterof interest (e.g., overlay) can also be measured or determined. Thussensitivity of the parameter (e.g., overlay) to aberrations can becalculated. Similarly, the sensitivity may be simulated using alithographic model (e.g., one of more of modules 71-75) and a metrologymodel. For example, a simulation may be performed by using a lithographymodel for every pertinent Zernike aberration where the aberration isvaried for a certain amount (e.g., several nm or a certain smallpercentage (e.g., 1-5%) to get a profile and the profile is provided toa metrology simulation to give a variation of an applicable parameter,e.g., overlay for variation in aberration and thus yield a sensitivity.

Further, in general, a goal of metrology target design is to design atarget that accurately simulates variation in a parameter of interestfor particular a product (e.g., device) design when exposed by aparticular lithographic apparatus. In other words, in an embodiment, fora particular product design being exposed using a particularlithographic apparatus, an optimal target design may be one whichminimizes the difference between variation in the parameter of interestfor the product design, par_(p), and variation in the parameter ofinterest for the metrology target design, par_(t). Thus, in anembodiment, this difference vis a vis optical aberrations can becalculated using the sensitivity, by using equation (1), as:

$\begin{matrix}{{\Delta \; {par}} = \sqrt{\sum_{i}\left( {{{par}_{p}()} - {\sum_{n}{{z_{n}()} \cdot \frac{\partial{par}_{t}}{\partial z_{n}}}}} \right)^{2}}} & (2)\end{matrix}$

In an embodiment, the parameter of interest for the product design,par_(p), (e.g. overlay) may be determined by simulation using alithographic model (e.g., one of more of modules 71-75) using theoptical system used to create the metrology target. The parameter ofinterest may be determined for specific slit positions or determined forthe whole slit (and optionally averaged over the slit for use in, forexample, equation (2)). The parameter of interest may be measured ifapplicable using an appropriate sensor and/or experimental setup.

FIG. 8 schematically depicts a method of designing a metrology target.The method includes, at block P101, determining the sensitivity of aparameter of interest for a metrology target to one or more of aplurality of optical aberrations, at block P102, determining theparameter of interest for a product design exposed using an opticalsystem of a lithographic apparatus, and at block P103, determining animpact on the parameter of interest based on the parameter for theproduct design and the sensitivity. In an embodiment, determining theimpact on the parameter of interest based on the sensitivity comprisesdetermining the impact based on the product of the sensitivity and oneor more of the respective aberrations of the optical system. In anembodiment, values of the one or more of the respective aberrations maybe at various particular positions, i, across the imaging slit of thelithographic apparatus. In an embodiment, the sensitivity of theparameter of interest to a particular aberration type is considered tobe linear within the design range of the optical aberration variationsin the lithographic apparatus.

Thus, the impact of variation in optical aberration over an exposureslit of the lithographic apparatus may be determined using the summationof the product of the sensitivity and its respective aberration value ofthe optical system across the slit using, e.g., using equation (1)and/or (2).

In an embodiment, the parameter of interest may be overlay error. In anembodiment, each of a plurality of optical aberrations is represented bya Zernike polynomial.

Accordingly, in an embodiment, a plurality of different metrology targetdesigns may be evaluated to determine an impact on one or moreparameters of the metrology target design using the method describedherein, to identify a metrology target design with the smallestdifference between the impact on the parameter for the target design andthe impact on the parameter for a product (device) design. Thus,beneficially, in an embodiment, the sensitivity of one or moreparameters to one of more optical aberration types may be simulatedinitially and optionally just once, e.g., the sensitivity of one or moreparameters to one of more optical aberration types may be simulated foreach of a plurality of metrology target designs. Then, the one or moreparameters of each of the metrology designs may be evaluated relative tothe parameter(s) of a product design, to determine the metrologytarget's suitability for that product design. So, different productdesigns may be evaluated without having to re-determine the sensitivityor performing a new simulation for the metrology target designs.Similarly, different aberration values for any different point in theslit may be evaluated and/or different combinations of aberration typesmay be evaluated, each without having to re-determine the sensitivity orperforming a new simulation for the metrology target. Thus, for example,a lithography and metrology simulation may not need to be repeated foreach point in the slit aberration profile and similarly, a lithographyand metrology simulation may not need to be repeated when the aberrationprofile is changed (e.g., for a different lithographic apparatus). Thelinear relationship of the sensitivity allows relatively simplespecification of the new aberration profile and/or aberration values todetermine the impact of aberration variation to a parameter for ametrology target design.

A plurality of metrology target designs can be ranked according to thevalue of impact on the one or more parameters. Such ranking may allow auser of the lithographic model to choose a particular design that maynot be the best ranked design, but is more suitable for the user'smanufacturing process. In an embodiment, where the parameter is overlay,a suitable metrology target design may be one that has less than orequal to 10 nm impact on overlay, for example less than or equal to 7 nmimpact, less than or equal to 5 nm impact, or less than or equal to 3 nmimpact.

FIG. 9 schematically depicts a further method of designing a metrologytarget. The method includes, at block P201, determining a sensitivity ofoverlay error of a metrology target design to one or more of a pluralityof aberration types. In an embodiment, each of the plurality of opticalaberrations is represented by a Zernike polynomial. At block 202, themethod further includes determining an overlay error impact of themetrology target design based on the sensitivity multiplied by therespective aberration value of an optical system of a lithographicapparatus to expose the metrology target. In an embodiment, determiningthe overlay error impact of the metrology target design is based on thesum of the sensitivities of a plurality of aberration types multipliedby the respective aberration values of an optical system of alithographic apparatus to expose the metrology target.

In an embodiment, the sensitivity(ies) of overlay error of the metrologytarget design is considered to be linear within the design range of theoptical aberration variations.

The impact on overlay error of variation in optical aberrations over theexposure slit of the lithographic apparatus may then be determined usingthe summation of the product of the sensitivity and its respectiveaberration for the plurality of aberrations of the optical system, e.g.,using:

$\begin{matrix}{{\Delta \; {ov}} = \sqrt{\sum_{i}\left( {{{ov}_{p}()} - {\sum_{n}{{z_{n}()} \cdot \frac{\partial{ov}_{t}}{\partial z_{n}}}}} \right)^{2}}} & (3)\end{matrix}$

wherein ov_(p)(i) is the overlay error for the product design atexposure slit position i, and ov_(t)(i) is the overlay error for thetarget design at exposure slit position i. A small as possible value ofΔov indicates the least overlay impact. In an embodiment, a suitablemetrology target design may be one that has a value of Δov less than orequal to 10 nm, for example less than or equal to 7 nm, less than orequal to 5 nm, or less than or equal to 3 nm.

In an embodiment, ov_(p)(i) may not be determined for a specificexposure slit position i. Rather, ov_(p)(i) may be the average valueover the exposure slit (and thus summed over the slit in equation (3)for the total value over the exposure slit).

In an embodiment, Δov is an example performance indicator of a metrologytarget design. Other performance indicators may be formulated. Forexample, a performance indicator may be formulated from equation (3) byomitting ov_(p)(i).

Accordingly, in an embodiment, a plurality of different metrology targetdesigns may be evaluated to determine an impact on overlay error of themetrology target design using the method described herein, to identify ametrology target design with the smallest difference between the impacton overlay error of the target design and the impact on the overlayerror of a product (device) design.

A plurality of metrology target designs can be ranked according to thevalue of impact on the one or more parameters. Such ranking may allow auser to choose a particular design that may not be the best rankeddesign, but is more suitable for the user's manufacturing process. In anembodiment, where the parameter is overlay, a suitable metrology targetdesign may be one that has less than or equal to 10 nm impact onoverlay, for example less than or equal to 7 nm impact, less than orequal to 5 nm impact, or less than or equal to 3 nm impact.

In an embodiment, one or more of the sensitivities may be weighteddifferent than other sensitivities. For example, the sensitivity for aparticular Zernike may be weighted more than the sensitivity for anotherparticular Zernike. In an embodiment, certain Zernike sensitivities maynot be determined or evaluated. For example, a spherical Zernike may nothave any overlay impact and thus its determination or evaluation may notbe necessary. Further, depending on the particular metrology targetdesign, a Zernike symmetrical in a particular direction (e.g., X or Ydirection) may not be determined or evaluated as it may have no overlayimpact in that particular direction for a particular metrology targetdesign.

Even though in this disclosure, Zernike terms are used as the primaryexample to demonstrate the methodology, this method can be generalizedto other representations of aberrations or even other lithographicparameters, for example, a pupil fit parameter which may contribute tononlinear CD response.

In sum, there may be provided a technique to facilitate quickerdetermination of an effective metrology target for a particular productdesign. It is desired to have the target sensitivity to aberrationsmatch the product sensitivity/behavior to aberrations. If they match,the target is a better predictor for the product. A problem is runninglengthy complex lithography and metrology simulations multiple times fornumerous target designs (and then doing it all again when theaberrations are changed, e.g., a different tool). It has been discoveredthat, in designing the target, a metrology target parameter (e.g.,target overlay) sensitivity to each Zernike

$\left( \frac{\partial{par}}{\partial z_{n}} \right.$

for the one or more Zernikes z_(n)) is generally linear within the rangeof lithographic apparatus aberration variations. Thus, it is possible toonly simulate once for a target to determine the parameter sensitivityto each Zernike. The parameter (e.g., overlay) impact of the target canthen be calculated as a sum of the Zernike sensitivities multiplied withthe particular Zernike amount (e.g., the Zernike amount at each of aplurality of positions in the slit of a particular tool). This can becombined with the parameter (e.g., overlay) of the product (e.g., ateach of the same plurality of positions in the slit) to yield aperformance indicator for the target. The process can be repeated for aplurality of target designs and then the target design with the bestperformance indicator value is the best match (for this criterion).

In an embodiment, a metrology target design can be evaluated so as todetermine whether the metrology target design has a similar sensitivityto an optical aberration parameter as a product design so that a betterprediction can be made of the product design when measuring the target.

Thus, as described above, the responsiveness or sensitivity of aparameter characterizing the product design and a metrology targetdesign to an optical aberration parameter (i.e., a measure of the changeof the value of parameter to a change in value of an optical aberrationparameter) can be measured or simulated. In an embodiment, thesensitivity can be measured or simulated per type of aberration.

A plurality of metrology target designs can then be evaluated to find ametrology target design that matches in terms of sensitivity with aproduct design. Such matching may specific to a particular aberration orto a set of aberrations. Thus, a collection of metrology target designswith their sensitivities relative to one or more aberrations may beprovided (e.g., determined from simulation) and from which to select adesired metrology target design. With the sensitivity of a productdesign to a specific set of aberrations determined (e.g., bysimulation), a metrology target design from the collection may then beidentified that matches the sensitivity of the product design (e.g., fora single aberration or a plurality of aberrations).

While the target structures described herein are metrology targetsspecifically designed and formed for the purposes of measurement, inother embodiments, properties may be measured on targets which arefunctional parts of devices formed on the substrate. Many devices haveregular, grating-like structures. The terms ‘target’, ‘target grating’and ‘target structure’ as used herein do not require that the structurehas been provided specifically for the measurement being performed.

While overlay targets in the form of gratings have been described, in anembodiment, other target types may be used such as box-in-box imagebased overlay targets.

While metrology targets to determine overlay have been primarilydescribed, the metrology targets may be used to determine, in thealternative or additionally, one of more other characteristics, such asfocus, dose, etc.

The metrology targets according to an embodiment may be designed ordefined using a data structure such as a pixel-based data structure or apolygon-based data structure. The polygon-based data structure may, forexample, be described using GDSII data formats, which are rather commonin the chip manufacturing industry. Still, any suitable data structureor data format may be used without departing from the scope of theembodiments. The metrology targets may be stored in a database fromwhich a user may select the required metrology target for use in aparticular semiconductor processing step. Such a database may comprise asingle metrology target or a plurality of metrology targets selected ordesigned according to the embodiments. The database may also comprise aplurality of metrology targets in which the database comprisesadditional information for each of the plurality of metrology targets.This additional information may comprise, for example, informationrelated to a suitability and/or a quality of the metrology target for aspecific lithographic process step and may even include suitabilityand/or quality of a single metrology target to different lithographicprocess steps. The suitability and/or quality of the metrology targetmay be expressed in a suitability value and/or a quality value,respectively, or any other value which may be used during a selectionprocess or a design process of a metrology target which is to be usedfor the specific lithographic process step.

In an embodiment, the computer readable medium may comprise instructionsfor activating at least some of the method steps using a connection tothe computer readable medium from a remote computer or from a remotesystem. Such connection may, for example, be generated over a securenetwork or via a (secure) connection over the world-wide-web (internet).In this embodiment, users may, for example, log in from a remotelocation to use the computer readable medium for determining asuitability and/or a quality of the metrology target design, or fordesigning a suitable metrology target design. The proposed parameter orparameters of the metrology target design may be provided by the remotecomputer (or by an operator using the remote computer to provide themetrology target design to the system for determining the suitability ofthe metrology target design or for determining the impact of themetrology target design on the parameter). So the proposed metrologytarget design may, for example, be simulated using models and may beowned by a different entity or company compared to the models usedduring the simulation process or determination process. Subsequently,the resulting determined impact to evaluate the metrology target qualitymay be provided back to the remote computer, for example, withoutleaving any residual details to excess the proposed parameters for themetrology target design or the simulation parameters used. In such anembodiment, a customer may acquire the option to run a design or anassessment of individually proposed metrology target designs withoutowning the software or having a copy of the software at its remotelocation. Such option may be obtained by, for example, a user agreement.A benefit of such user agreement may be that the models used in thesimulations may always be the most recent and/or the most detailedmodels available without the need to locally update any software.Furthermore, by separating the model simulation and the proposedparameters of the metrology target design or metrology target proposal,the details of the designed markers or the different layers used for theprocessing need not to be shared by the two companies.

In association with the physical grating structures of the targets asrealized on substrates and patterning devices, an embodiment may includea computer program containing one or more sequences of machine-readableinstructions describing a method of designing a target, producing atarget on a substrate, measuring a target on a substrate and/oranalyzing measurements to obtain information about a lithographicprocess. This computer program may be executed for example within unitPU in the apparatus of FIGS. 3 and 4 and/or the control unit LACU ofFIG. 2. There may also be provided a data storage medium (e.g.,semiconductor memory, magnetic or optical disk) having such a computerprogram stored therein. Where an existing apparatus, for example of thetype shown in FIGS. 1-4, is already in production and/or in use, anembodiment can be implemented by the provision of updated computerprogram products for causing a processor of the apparatus to perform amethod as described herein.

An embodiment of the invention may take the form of a computer programcontaining one or more sequences of machine-readable instructionsdescribing a method as disclosed herein, or a data storage medium (e.g.semiconductor memory, magnetic or optical disk) having such a computerprogram stored therein. Further, the machine readable instruction may beembodied in two or more computer programs. The two or more computerprograms may be stored on one or more different memories and/or datastorage media.

Any controllers described herein may each or in combination be operablewhen the one or more computer programs are read by one or more computerprocessors located within at least one component of the lithographicapparatus. The controllers may each or in combination have any suitableconfiguration for receiving, processing, and sending signals. One ormore processors are configured to communicate with the at least one ofthe controllers. For example, each controller may include one or moreprocessors for executing the computer programs that includemachine-readable instructions for the methods described above. Thecontrollers may include data storage medium for storing such computerprograms, and/or hardware to receive such medium. So the controller(s)may operate according the machine readable instructions of one or morecomputer programs.

The invention may further be described using the following clauses:

1. A method of metrology target design, the method comprising:

determining a sensitivity of a parameter for a metrology target designto an optical aberration; and

determining an impact on the parameter of the metrology target designbased on the parameter for a product design exposed using an opticalsystem of a lithographic apparatus and the product of the sensitivityand the respective aberration of the optical system.

2. The method of clause 1, comprising determining a sensitivity of aparameter for a metrology target design to each of a plurality ofoptical aberrations and determining an impact on the parameter of themetrology target design based on the parameter for the product designand the product of the sensitivities and the respective aberrations ofthe optical system.3. The method of clause 1 or clause 2, further comprising determiningthe parameter for the product design exposed using the optical system ofthe lithographic apparatus.4. The method of clause 3, further comprising determining the parameterfor the product design by simulating the product design as exposed usingthe optical system.5. The method of any of clauses 1 to 4, wherein determining thesensitivity is performed by simulation using a lithographic model.6. The method of any of clauses 1 to 5, wherein the parameter comprisesoverlay error.7. The method of any of clauses 1 to 6, wherein the optical aberrationcomprises a Zernike polynomial.8. The method of any of clauses 1 to 7, wherein determining the impactcomprises summation, for a plurality of positions of an exposure slit ofthe lithographic apparatus, of the product of the sensitivity and itsrespective aberration of the optical system.9. The method of any of clauses 1 to 8, wherein the sensitivity isconsidered to be linear within a design range of the optical systemaberration variations.10. The method of any of clauses 1 to 9, comprising performing thedetermining for a plurality of different metrology target designs toidentify a metrology target design with a smallest difference betweenthe parameter for the metrology target design and the parameter for theproduct design.11. A method of metrology target design, the method comprising:

determining a sensitivity of overlay error of a metrology target designto a respective aberration of a plurality of aberrations; and

determining an overlay error impact of the metrology target design basedon the sum of the sensitivities multiplied by the respective aberrationsof an optical system of a lithographic apparatus to expose the metrologytarget.

12. The method of clause 11, wherein the aberrations respectivelycomprise a Zernike polynomial.13. The method of clause 11 or clause 12, wherein the sensitivities areconsidered to be linear within a design range of the optical systemaberration variations.14. The method of any of clauses 11 to 13, wherein determining thesensitivity is performed by simulation using a lithographic model.15. The method of any of clauses 11 to 14, further comprising simulatingan overlay error of a product design exposed using the optical system.16. The method of any of clauses 11 to 15, wherein determining theimpact comprises summation, for a plurality of positions of an exposureslit of the lithographic apparatus, of the product of the sensitivitiesand the respective aberrations of the optical system.17. A computer readable medium comprising instructions executable by acomputer to perform a method according to any of clauses 1 to 16.18. The computer readable medium of clause 17, wherein the instructionsexecutable by the computer further comprise instructions for activatingat least some of the method steps using a connection to the computerreadable medium from a remote computer.19. The computer readable medium of clause 18, wherein the connectionwith the remote computer is a secured connection.20. The computer readable medium of any of the clauses 18 and 19,wherein the parameter of the metrology target design is provided by theremote computer.21. The computer readable medium of clause 20, wherein the method isfurther configured for providing the impact on the parameter of themetrology design back to the remote computer.22. A system of metrology target design for use on a substrate, thesystem comprising:

a processing unit configured and arranged to:

determining a sensitivity of a parameter for a metrology target designto an optical aberration; and

determining an impact on the parameter of the metrology target designbased on the parameter for a product design exposed using an opticalsystem of a lithographic apparatus and the product of the sensitivityand the respective aberration of the optical system.

-   -   23. The system according to clause 22, wherein the system        comprises an connection to a network for communicating with a        remote system.        24. The system according to clause 23, wherein the remote system        is configured for providing the parameter for the metrology        target design to the system.        25. The system according to clause 23 or 24, wherein the system        is configured for using the connection to the remote system for        transmitting the impact on the parameter of the metrology target        design back to the remote system.        26. A metrology target configured for being measured using a        metrology measurement system, the metrology target being        designed or selected by the method of any of the clauses 1 to 16        or by the computer readable medium of any of the clauses 17 to        21.        27. The metrology target according to clause 26, wherein the        metrology measurement system comprises a diffraction based        measurement system.        28. A metrology measurement system using the metrology target        designed or selected by the method of any of the clauses 1 to 16        or by the computer readable medium of any of the clauses 17 to        21.        29 A metrology measurement system configured for measuring the        metrology target designed or selected by the method of any of        the clauses 1 to 16 or by the computer readable medium of any of        the clauses 17 to 21.        30. A substrate comprising the metrology target designed or        selected by the method of any of the clauses 1 to 16 or by the        computer readable medium of any of the clauses 17 to 21.        31. The substrate according to clause 30, wherein the substrate        is a wafer comprising at least some of the layers of an        integrated circuit.        32. A lithographic imaging apparatus configured for imaging a        metrology target designed or selected by the method of any of        the clauses 1 to 16 or by the computer readable medium of any of        the clauses 17 to 21.        33. A lithographic imaging apparatus configured for imaging a        metrology target according to any of the clauses 26 and 27.        34. A data structure representing the metrology target designed        or selected by the method of any of the clauses 1 to 16 or by        the computer readable medium of any of the clauses 17 to 21.        35. A data structure representing the metrology target according        to any of the clauses 26 and 27.        36. A database comprising the metrology target designed or        selected by the method of any of the clauses 1 to 16 or by the        computer readable medium of any of the clauses 17 to 21.        37. The database according to clause 36, wherein the database        comprises a plurality of metrology targets, each designed or        selected by the method of any of the clauses 1 to 16 or by the        computer readable medium of any of the clauses 17 to 21.        38. A database comprising the data structure according to any of        the clauses 34 and 35.        39. The database according to clause 38, wherein the database        comprises a plurality of data structures each representing the        metrology target designed or selected by the method of any of        the clauses 1 to 16 or by the computer readable medium of any of        the clauses 17 to 21.        40. The database according to any of the clauses 36 to 39,        wherein the database comprises a suitability value associated        with the metrology target design, the suitability value        indicating a suitability of the metrology target design for a        lithographic process step.        41. A data carrier comprising the data structure according to        any of the clauses 34 and 35 and/or comprising the database        according to any of the clauses 36 to 40.        42. Use of the metrology target according to any of the clauses        26 and 27, wherein the metrology target is used for determining        a positioning of one layer relative to another layer on the        substrate, and/or for determining an alignment of a layer on the        substrate relative to the projection optics of a lithographic        imaging apparatus, and/or for determining a critical dimension        of a structure on the substrate.

Although specific reference may have been made above to the use ofembodiments in the context of optical lithography, it will beappreciated that an embodiment of the invention may be used in otherapplications, for example imprint lithography, and where the contextallows, is not limited to optical lithography. In imprint lithography, atopography in a patterning device defines the pattern created on asubstrate. The topography of the patterning device may be pressed into alayer of resist supplied to the substrate whereupon the resist is curedby applying electromagnetic radiation, heat, pressure or a combinationthereof. The patterning device is moved out of the resist leaving apattern in it after the resist is cured.

Further, although specific reference may be made in this text to the useof lithographic apparatus in the manufacture of ICs, it should beunderstood that the lithographic apparatus described herein may haveother applications, such as the manufacture of integrated opticalsystems, guidance and detection patterns for magnetic domain memories,flat-panel displays, liquid-crystal displays (LCDs), thin film magneticheads, etc. The skilled artisan will appreciate that, in the context ofsuch alternative applications, any use of the terms “wafer” or “die”herein may be considered as synonymous with the more general terms“substrate” or “target portion”, respectively. The substrate referred toherein may be processed, before or after exposure, in for example atrack (a tool that typically applies a layer of resist to a substrateand develops the exposed resist), a metrology tool and/or an inspectiontool. Where applicable, the disclosure herein may be applied to such andother substrate processing tools. Further, the substrate may beprocessed more than once, for example in order to create a multi-layerIC, so that the term substrate used herein may also refer to a substratethat already contains multiple processed layers.

The terms “radiation” and “beam” used herein encompass all types ofelectromagnetic radiation, including ultraviolet (UV) radiation (e.g.having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) andextreme ultra-violet (EUV) radiation (e.g. having a wavelength in therange of 5-20 nm), as well as particle beams, such as ion beams orelectron beams.

The term “lens”, where the context allows, may refer to any one orcombination of various types of optical components, includingrefractive, reflective, magnetic, electromagnetic and electrostaticoptical components.

The descriptions above are intended to be illustrative, not limiting.Thus, it will be apparent to one skilled in the art that modificationsmay be made to the invention as described without departing from thescope of the claims set out below. For example, one or more aspects ofone or more embodiments may be combined with or substituted for one ormore aspects of one or more other embodiments as appropriate. Therefore,such adaptations and modifications are intended to be within the meaningand range of equivalents of the disclosed embodiments, based on theteaching and guidance presented herein. It is to be understood that thephraseology or terminology herein is for the purpose of description byexample, and not of limitation, such that the terminology or phraseologyof the present specification is to be interpreted by the skilled artisanin light of the teachings and guidance. The breadth and scope of theinvention should not be limited by any of the above-described exemplaryembodiments, but should be defined only in accordance with the followingclaims and their equivalents.

1.-18. (canceled)
 19. A system of metrology target structure design, thesystem comprising: a hardware processing unit; a non-transitory computerreadable medium comprising instructions executable by the hardwareprocessing unit to: determine a value of a sensitivity of a parameter ofa design of a metrology target structure to each respective aberrationof a plurality of aberrations, wherein the metrology target structure isused for metrology in the manufacture of physical devices; and determinean impact of the metrology target structure design on the parameterbased on a sum of values that are equivalent to the values of thesensitivities multiplied by values of respective aberrations of anoptical system of a lithographic apparatus used to expose the metrologytarget structure.
 20. The system of claim 19, wherein the aberrationsrespectively comprise a Zernike polynomial.
 21. The system of claim 19,wherein the sensitivities are considered to be linear within a designrange of the optical system aberration variations.
 22. The system ofclaim 19, wherein the instructions executable by the hardware processingunit to determine the values of the sensitivity are configured todetermine the values of the sensitivity by simulation using alithographic model.
 23. The system of claim 19, further comprisinginstructions executable by the hardware processing unit to simulate theparameter of a device product design exposed using the optical system.24. The system of claim 19, wherein the instructions executable by thehardware processing unit to determine the impact are configured todetermine the impact by summation, for a plurality of positions of anexposure slit of the lithographic apparatus, of values that areequivalent to the values of the sensitivities multiplied by values ofrespective optical aberrations of the optical system.
 25. The system ofclaim 19, further comprising a connection to a network for communicatingwith a remote system.
 26. The system of claim 25, wherein the remotesystem is configured to provide the parameter for the metrology targetstructure design to the system.
 27. The system of claim 25, wherein thesystem is configured to use the connection to the remote system totransmit the impact on the parameter of the metrology target design backto the remote system.
 28. The system of claim 19, wherein theinstructions executable by the hardware processing are furtherconfigured to select the metrology target structure design based on theimpact and measure the metrology structure of the selected metrologytarget design in the manufacture of physical devices.
 29. A method ofmetrology target structure design, the method comprising: determining avalue of a sensitivity of a parameter pertaining to a design of ametrology target structure to each respective aberration of a pluralityof aberrations, wherein the metrology target structure is used formetrology in the manufacture of physical devices; and determining, by ahardware computer system, an impact of the metrology target structuredesign on the parameter based on a sum of values that are equivalent tothe values of the sensitivities multiplied by values of respectiveaberrations of an optical system of a lithographic apparatus used toexpose the metrology target structure.
 30. The method of claim 29,wherein the aberrations respectively comprise a Zernike polynomial. 31.The method of claim 29, wherein the sensitivities are considered to belinear within a design range of the optical system aberrationvariations.
 32. The method of claim 29, wherein determining the valuesof the sensitivity is performed by simulation using a lithographicmodel.
 33. The method of claim 29, further comprising obtaining bysimulation a value of the parameter for a device product design exposedusing the optical system.
 34. The method of claim 29, whereindetermining the impact comprises summation, for a plurality of positionsof an exposure slit of the lithographic apparatus, of values that areequivalent to the values of the sensitivities multiplied by values ofrespective optical aberrations of the optical system.
 35. The method ofclaim 29, further comprising selecting the metrology target structuredesign based on the impact and measuring the metrology structure of theselected metrology target design in the manufacture of physical devices.36. A non-transitory computer readable medium comprising instructionsexecutable by a hardware computer to: determine a value of a sensitivityof a parameter pertaining to a design of a metrology target structure toeach respective aberration of a plurality of aberrations, wherein themetrology target structure is used for metrology in the manufacture ofphysical devices; and determine an impact of the metrology targetstructure design on the parameter based on a sum of values that areequivalent to the values of the sensitivities multiplied by values ofrespective aberrations of an optical system of a lithographic apparatusused to expose the metrology target structure.
 37. The medium of claim36, wherein the sensitivities are considered to be linear within adesign range of the optical system aberration variations.
 38. The mediumof claim 36, wherein the instructions executable by the hardwarecomputer to determine the values of the sensitivity are configured todetermine the values of the sensitivity by simulation using alithographic model.